Inversions of landslide strength as a proxy for subsurface weathering

Distributions of landslide size are hypothesized to reflect hillslope strength, and consequently weathering patterns. However, the association of weathering and critical zone architecture with mechanical strength properties of parent rock and soil are poorly-constrained. Here we use three-dimensional stability to analyze 7330 landslides in western Oregon to infer combinations of strength - friction angles and cohesion - through analysis of both failed and reconstructed landslide terrain. Under a range of conditions, our results demonstrate that the failure envelope that relates shear strength and normal stress in landslide terrain is nonlinear owing to an exchange in strength with landslide thickness. Despite the variability in material strength at large scales, the observed gradient in proportional cohesive strength with landslide thickness may serve as a proxy for subsurface weathering. We posit that the observed relationships between strength and landslide thickness are associated with the coalescence of zones of low shear strength driven by fractures and weathering, which constitutes a first-order control on the mechanical behavior of underlying soil and rock mass.

Relationships between landslide area versus strength and mean landslide thickness versus strength for a suite of groundwater conditions. We consider dry conditions, groundwater depths of 20m, 10m, 5m, 2m, 1m, 0.5m, and full saturation (0 m depth to groundwater). The exchange in proportional frictional and cohesive strength is largely insensitive to the groundwater conditions shown, although a modest increase in cohesive resistance is observed with decreasing groundwater depth. No evident exchange in proportional strength is observed for the range of landslide areas shown, but the trends are more apparent when comparing proportional strength to mean landslide thickness. Magnitudes of shear strength are sensitive to groundwater conditions. Generally, a modest decrease in friction angle and significant increase in cohesion is observed with increasing mean landslide thickness, but is diminished for discrete groundwater depths. A decrease in friction angle and modest gain in cohesion is shown with increasing landslide area for all groundwater conditions. Figure SI.8. Relationships between mean landslide thickness versus strength for a suite of saturation ratios (m). We consider dry conditions, pore pressure ratios of 0.25, 0.5, 0.75, and full saturation. Comparatively, the exchange in proportional frictional and cohesive strength is largely insensitive to the pore pressure ratios shown, although a modest increase in cohesive resistance is observed with increasing ru. Magnitudes of shear strength are sensitive to m. Generally, a modest decrease in friction angle and significant increase in cohesion is observed with increasing mean landslide thickness.
Figure SI.9. Distributions of strength (effective friction angle, ′, and cohesion, ′) and landslide morphology (mean thickness, , and mean surface inclination, ) for n landslide samples by Varnes landslide classification (DOGAMI 2009). Bedrock landslides and particularly landslide complexes demonstrate higher mean thickness and cohesion than their soil/debris counterparts. Modest differences are shown between median rock and soil/debris landslide friction angles, but generally the higher percentiles of soil/debris are higher than bedrock counterparts.

Rock Flows
Table SI.2b. Wilcoxon rank sum test comparing cohesion distributions of different landslide classifications and their level of statistical significance of their differences. A (-) reflects no statistical difference under a 5% significance level, (*) represents statistical differences under a 5% significance level, (**) represents statistical differences under a 1% significance level, and (***) represents statistical differences under a 0.1% significance level. A nonlinear failure envelope is shown for most potential groundwater conditions (the exception being groundwater depths of 10m and 20m). In some cases, relationships between friction angle are relatively insensitive to normal effective stress (e.g. groundwater depths of 1 m to 20 m), but nonlinearity is maintained as a function of cohesion.  Approximately 25% of landslides have a mean thickness of less than 1m (predominantly soil), while 70% have mean thicknesses of 1 to 10 m (predominantly saprolite, weathered bedrock and potentially fresh bedrock). (b) Proportion of total shear strength (unitless, 0 to 1) attributed to cohesion and friction in comparison to landslide thickness. The shaded areas represent the bounds between 10 th and 90 th moving percentiles (1% bins of all data) of cohesive and frictional resistance, respectively. A gradual transfer from frictional resistance to cohesive resistance is observed with increasing landslide thickness, the largest exchange occurring within weathered bedrock suggestive of a depth of potentially aggressive weathering and strength change. (c) Exchange in friction angle and cohesion with mean landslide thickness.
Figure SI.14. (a) Fitted failure envelopes for 10 th , 50 th and 90 th percentiles based on bins of 1% of all effective normal stress data for friction angles determined only from the landslide source area (i.e. no back-analysis of cohesion) for m=0.5 conditions. The failure envelope is still nonlinear, reflecting the importance of effective normal stress (a function of groundwater, inclination, and mean landslide thickness) on governing shear strength. The nonlinear envelope is similar to those proposed for rock (i.e. Barton 2006). (b) The nonlinearity for this specific set of assumptions and conditions stems from a nonlinear decrease in friction angle with effective normal stress, as shown for 1% bins of all effective normal stress data.  (Roering et al. 2003). For management conditions of No Roots,Clearcut,Industrial Forest,and Natural Forest,root cohesions were 0,3.35,7.66,and 54.89 kPa, respectively. Lateral root cohesion was only applied to the area of the rupture surface with depths of 0.5 m or less, consistent with the general shallow rooting depths described by Roering et al. (2003). These root cohesion values have been conjectured to possible overestimate the mechanical reinforcement of roots (by as much as 75%) owing to their progressive breakage and pullout (e.g. Pollen et al. 2005, Cohen et al. 2011, Giarossich et al. 2019, thus reflect an upper bound for the proposed management conditions. As shown, stronger root cohesions amplify the proposed exchange between frictional and cohesive resistance with landslide thickness as much of the back-analyzed mineral cohesion is now supported by lateral root cohesion. This sensitivity analysis tests the possibility that landslide deposits are stable and consequently not in a state of limiting equilibrium. As shown, increased FS applied to deposit friction angles yields lower cohesion values and offsets the exchange between cohesive and frictional resistance, but an exchange is still present. . This distribution shows that the median FS for deposits would be ≈1.26, which is on par with the stability of engineered slopes (Allen 2015). As landslide deposits are often prone to continued failure from being placed in a precarious state (Temme et al. 2020), such a high FS is possible, but perhaps not always likely. This suggests that back-analysis of friction from deposits and subsequent use for back-analysis of cohesion from source areas, while an assumption, may serve as a reasonable technique to glean first order estimates of unique cohesion and friction pairs for landslide inventories.
Figure SI.18. Strength relationships versus mean annual precipitation and modeled peak ground acceleration (PGA) for a Mw 9.0 earthquake. As shown there are no clear trends between PGA and friction or cohesion, suggesting that there is no obvious control of coseismic triggering in the landslide inventories. A modest trend between mean annual rainfall and strength does persist (i.e. higher strength for more rainfall). where the friction angle for existing topography was smaller than that from reconstructed terrain (≈14% of all landslides). As shown, similar trends to those presented still persist, although the exchange of proportional strength with mean landslide thickness is slightly more gradual.